Finite Group Databasebeta

← C5×#14185 #11936905

Subgroups — C5×#14185 #11936905

Order 1280.

2422 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×D4C211yesmaximal, characteristic
2C2×C5×#394C211yesmaximal, characteristic
3C2×C5×#389C211yesmaximal, characteristic, complemented
4C2×C5×#388C211yesmaximal, characteristic, complemented
5C2×C5×#385C211yesmaximal, characteristic, complemented
6C2×C5×#385C211yesmaximal, characteristic, complemented
7C2×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
8C5×#1440C211yesmaximal, characteristic, complemented
9C5×#1439C211yesmaximal, characteristic, complemented
10C5×#1438C211yesmaximal, characteristic
11C5×#1437C211yesmaximal, characteristic, complemented
12C5×#1436C211yesmaximal, characteristic, complemented
13C5×#1436C211yesmaximal, characteristic, complemented
14C5×#1436C211yesmaximal, characteristic, complemented
15C5×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C5×D4C2211yescharacteristic
17C24×C4×C5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C2×C4×C5×D4—24no—
20C2×C4×C5×D4—24no—
21C2×C4×C5×D4—24no—
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C5×C22⋊C4C2211yescharacteristic
32C22×C5×C22⋊C4C2211yescharacteristic
33C22×C5×C22⋊C4C2211yescharacteristic
34C22×C5×C22⋊C4C2211yescharacteristic
35C22×C5×C22⋊C4C2211yescharacteristic
36C22×C5×C22⋊C4C2211yescharacteristic
37C22×C42×C5C2211yescharacteristic
38C22×C42×C5C2211yescharacteristic
39C22×C42×C5C2211yescharacteristic
40C5×#394C418yescomplemented
41C5×#389—24no—
42C5×#388—24no—
43C5×#385—24no—
44C5×#385—24no—
45C4×C5×C22⋊C4—24no—
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×C5×#95C2211yescharacteristic
58C2×C5×#95C2211yescharacteristic
59C2×C5×#95C2211yescharacteristic
60#14185C511yesmaximal, characteristic, direct product factor, Sylow
61C25×C5C2311yescharacteristic
62C25×C5C2311yescharacteristic
63C22×C5×D4—22no—
64C22×C5×D4—22no—
65C22×C5×D4—22no—
66C22×C5×D4—22no—
67C22×C5×D4—22no—
68C22×C5×D4—22no—
69C22×C5×D4C2×C414yes—
70C23×C4×C5—22no—
71C23×C4×C5—22no—
72C23×C4×C5—22no—
73C23×C4×C5—22no—
74C23×C4×C5—22no—
75C23×C4×C5—22no—
76C23×C4×C5—22no—
77C23×C4×C5—22no—
78C23×C4×C5—22no—
79C23×C4×C5—41no—
80C23×C4×C5—41no—
81C23×C4×C5—41no—
82C23×C4×C5—41no—
83C23×C4×C5D414yes—
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2311yescharacteristic
93C23×C4×C5C2311yescharacteristic
94C23×C4×C5C2311yescharacteristic
95C23×C4×C5C2311yescharacteristic
96C23×C4×C5C2311yescharacteristic
97C4×C5×D4—232no—
98C2×C5×C4⋊C4—22no—
99C2×C5×C4⋊C4—22no—
100C2×C5×C4⋊C4—22no—
101C2×C5×C4⋊C4—22no—
102C2×C5×C4⋊C4—22no—
103C2×C5×C4⋊C4—22no—
104C2×C5×C4⋊C4—22no—
105C2×C5×C4⋊C4—22no—
106C2×C5×C4⋊C4—22no—
107C2×C5×C4⋊C4—22no—
108C2×C5×C4⋊C4—22no—
109C2×C5×C4⋊C4—22no—
110C2×C5×C4⋊C4—41no—
111C2×C5×C4⋊C4C2×C414yescomplemented
112C2×C5×C4⋊C4D414yes—
113C2×C5×C22⋊C4—22no—
114C2×C5×C22⋊C4—22no—
115C2×C5×C22⋊C4—22no—
116C2×C5×C22⋊C4—22no—
117C2×C5×C22⋊C4—22no—
118C2×C5×C22⋊C4—22no—
119C2×C5×C22⋊C4—22no—
120C2×C5×C22⋊C4—22no—
121C2×C5×C22⋊C4—22no—
122C2×C5×C22⋊C4—22no—
123C2×C5×C22⋊C4—22no—
124C2×C5×C22⋊C4—22no—
125C2×C5×C22⋊C4—22no—
126C2×C5×C22⋊C4—22no—
127C2×C5×C22⋊C4—22no—
128C2×C5×C22⋊C4—22no—
129C2×C5×C22⋊C4—22no—
130C2×C5×C22⋊C4—22no—
131C2×C5×C22⋊C4—22no—
132C2×C5×C22⋊C4—22no—
133C2×C5×C22⋊C4—22no—
134C2×C5×C22⋊C4—41no—
135C2×C5×C22⋊C4—41no—
136C2×C5×C22⋊C4—41no—
137C2×C5×C22⋊C4—41no—
138C2×C5×C22⋊C4C2×C414yescomplemented
139C2×C5×C22⋊C4C2×C414yescomplemented
140C2×C5×C22⋊C4C2×C414yescomplemented
141C2×C5×C22⋊C4C2×C414yescomplemented
142C2×C5×C22⋊C4D414yes—
143C2×C42×C5—22no—
144C2×C42×C5—22no—
145C2×C42×C5—22no—
146C2×C42×C5—22no—
147C2×C42×C5—22no—
148C2×C42×C5—22no—
149C2×C42×C5—22no—
150C2×C42×C5—41no—
151C2×C42×C5—41no—
152C5×#95—22no—
153C5×#95—22no—
154C5×#95—22no—
155C5×#95—22no—
156C5×#95—22no—
157C5×#95—22no—
158C5×#95—22no—
159C5×#95—22no—
160C5×#95—22no—
161C5×#95—22no—
162C5×#95—22no—
163C5×#95—41no—
164C5×#95C2×C414yescomplemented
165C5×#95D414yescomplemented
166C22×C4×D4C2×C511yescharacteristic
167C2×#394C2×C511yescharacteristic
168C2×#389C2×C511yescharacteristic, complemented
169C2×#388C2×C511yescharacteristic, complemented
170C2×#385C2×C511yescharacteristic, complemented
171C2×#385C2×C511yescharacteristic, complemented
172C2×C4×C22⋊C4C2×C511yescharacteristic, complemented
173#1440C2×C511yescharacteristic, complemented
174#1439C2×C511yescharacteristic, complemented
175#1438C2×C511yescharacteristic
176#1437C2×C511yescharacteristic, complemented
177#1436C2×C511yescharacteristic, complemented
178#1436C2×C511yescharacteristic, complemented
179#1436C2×C511yescharacteristic, complemented
180C22⋊#95C2×C511yescharacteristic, complemented
181C24×C5—21no—
182C24×C5—21no—
183C24×C5—21no—
184C24×C5—21no—
185C24×C5—21no—
186C24×C5—21no—
187C24×C5—21no—
188C24×C5—21no—
189C24×C5—21no—
190C24×C5—21no—
191C24×C5—21no—
192C24×C5—21no—
193C24×C5—21no—
194C24×C5—21no—
195C24×C5—21no—
196C24×C5—21no—
197C24×C5—21no—
198C24×C5—21no—
199C24×C5—21no—
200C24×C5—21no—
201C24×C5—21no—
202C24×C5—21no—
203C24×C5—21no—
204C24×C5—21no—
205C24×C5C22×C412yes—
206C24×C5C22×C412yes—
207C24×C5C2×D412yes—
208C24×C5C2×D412yes—
209C24×C5#4112yes—
210C24×C5#4112yes—
211C24×C5C2411yescharacteristic
212C2×C5×D4—28no—
213C2×C5×D4—28no—
214C2×C5×D4—28no—
215C2×C5×D4—28no—
216C2×C5×D4—28no—
217C2×C5×D4—28no—
218C2×C5×D4—28no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—21no—
228C22×C4×C5—21no—
229C22×C4×C5—21no—
230C22×C4×C5—21no—
231C22×C4×C5—21no—
232C22×C4×C5—21no—
233C22×C4×C5—21no—
234C22×C4×C5—21no—
235C22×C4×C5—28no—
236C22×C4×C5—21no—
237C22×C4×C5—21no—
238C22×C4×C5—21no—
239C22×C4×C5—21no—
240C22×C4×C5—21no—
241C22×C4×C5—21no—
242C22×C4×C5—21no—
243C22×C4×C5—21no—
244C22×C4×C5—21no—
245C22×C4×C5—21no—
246C22×C4×C5—21no—
247C22×C4×C5—21no—
248C22×C4×C5—21no—
249C22×C4×C5—21no—
250C22×C4×C5—21no—
251C22×C4×C5—21no—
252C22×C4×C5—21no—
253C22×C4×C5—21no—
254C22×C4×C5—21no—
255C22×C4×C5—21no—
256C22×C4×C5—21no—
257C22×C4×C5—21no—
258C22×C4×C5—21no—
259C22×C4×C5—21no—
260C22×C4×C5—21no—
261C22×C4×C5—21no—
262C22×C4×C5—21no—
263C22×C4×C5—21no—
264C22×C4×C5—21no—
265C22×C4×C5—21no—
266C22×C4×C5—21no—
267C22×C4×C5—21no—
268C22×C4×C5—21no—
269C22×C4×C5—21no—
270C22×C4×C5—21no—
271C22×C4×C5—21no—
272C22×C4×C5—21no—
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—21no—
277C22×C4×C5—21no—
278C22×C4×C5—28no—
279C22×C4×C5—28no—
280C22×C4×C5—21no—
281C22×C4×C5—21no—
282C22×C4×C5—21no—
283C22×C4×C5—21no—
284C22×C4×C5—21no—
285C22×C4×C5—21no—
286C22×C4×C5—21no—
287C22×C4×C5—21no—
288C22×C4×C5—21no—
289C22×C4×C5—21no—
290C22×C4×C5—21no—
291C22×C4×C5—21no—
292C22×C4×C5—21no—
293C22×C4×C5—21no—
294C22×C4×C5—44no—
295C22×C4×C5—44no—
296C22×C4×C5—44no—
297C22×C4×C5—44no—
298C22×C4×C5—44no—
299C22×C4×C5—44no—
300C22×C4×C5—44no—
301C22×C4×C5—44no—
302C22×C4×C5—44no—
303C22×C4×C5—44no—
304C22×C4×C5—44no—
305C22×C4×C5C22×C412yes—
306C22×C4×C5C22×C412yes—
307C22×C4×C5C22×C412yes—
308C22×C4×C5C22×C412yes—
309C22×C4×C5C22×C412yes—
310C22×C4×C5C2×D412yes—
311C22×C4×C5C2×D412yes—
312C22×C4×C5C2×D412yes—
313C22×C4×C5C2×D412yes—
314C22×C4×C5C2×D412yes—
315C22×C4×C5C2×D412yes—
316C22×C4×C5C2×D412yes—
317C22×C4×C5C2×D412yes—
318C22×C4×C5C2×D412yes—
319C22×C4×C5C2×D412yes—
320C22×C4×C5#4112yes—
321C22×C4×C5#4112yes—
322C22×C4×C5#4112yes—
323C22×C4×C5#4112yes—
324C5×C4⋊C4—28no—
325C5×C4⋊C4—28no—
326C5×C4⋊C4—44no—
327C5×C4⋊C4—44no—
328C5×C4⋊C4—44no—
329C5×C22⋊C4—28no—
330C5×C22⋊C4—28no—
331C5×C22⋊C4—28no—
332C5×C22⋊C4—28no—
333C5×C22⋊C4—28no—
334C5×C22⋊C4—28no—
335C5×C22⋊C4—28no—
336C5×C22⋊C4—44no—
337C5×C22⋊C4—44no—
338C5×C22⋊C4—44no—
339C42×C5—28no—
340C42×C5—44no—
341C42×C5—44no—
342C23×D4C22×C511yescharacteristic
343C24×C4C22×C511yescharacteristic
344C24×C4C22×C511yescharacteristic
345C2×C4×D4—24no—
346C2×C4×D4—24no—
347C2×C4×D4—24no—
348C22×C4⋊C4C22×C511yescharacteristic
349C22×C4⋊C4C22×C511yescharacteristic
350C22×C4⋊C4C22×C511yescharacteristic
351C22×C4⋊C4C22×C511yescharacteristic
352C22×C4⋊C4C22×C511yescharacteristic
353C22×C22⋊C4C22×C511yescharacteristic
354C22×C22⋊C4C22×C511yescharacteristic
355C22×C22⋊C4C22×C511yescharacteristic
356C22×C22⋊C4C22×C511yescharacteristic
357C22×C22⋊C4C22×C511yescharacteristic
358C22×C22⋊C4C22×C511yescharacteristic
359C22×C22⋊C4C22×C511yescharacteristic
360C22×C22⋊C4C22×C511yescharacteristic
361C22×C22⋊C4C22×C511yescharacteristic
362C22×C22⋊C4C22×C511yescharacteristic
363C22×C42C22×C511yescharacteristic
364C22×C42C22×C511yescharacteristic
365C22×C42C22×C511yescharacteristic
366#394C4×C518yescomplemented
367#389—24no—
368#388—24no—
369#385—24no—
370#385—24no—
371C4×C22⋊C4—24no—
372C2×#95C22×C511yescharacteristic
373C2×#95C22×C511yescharacteristic
374C2×#95C22×C511yescharacteristic
375C2×#95C22×C511yescharacteristic
376C2×#95C22×C511yescharacteristic
377C2×#95C22×C511yescharacteristic
378C2×#95C22×C511yescharacteristic
379C2×#95C22×C511yescharacteristic
380C2×#95C22×C511yescharacteristic
381C2×#95C22×C511yescharacteristic
382C2×#95C22×C511yescharacteristic
383C2×#95C22×C511yescharacteristic
384C2×#95C22×C511yescharacteristic
385C2×#95C22×C511yescharacteristic
386C23×C5—22no—
387C23×C5—22no—
388C23×C5—22no—
389C23×C5—22no—
390C23×C5—22no—
391C23×C5—22no—
392C23×C5—22no—
393C23×C5—22no—
394C23×C5—22no—
395C23×C5—22no—
396C23×C5—22no—
397C23×C5—22no—
398C23×C5—22no—
399C23×C5—22no—
400C23×C5—22no—
401C23×C5—22no—
402C23×C5—22no—
403C23×C5—22no—
404C23×C5—22no—
405C23×C5—22no—
406C23×C5—22no—
407C23×C5—22no—
408C23×C5—22no—
409C23×C5—22no—
410C23×C5—22no—
411C23×C5—22no—
412C23×C5—22no—
413C23×C5—22no—
414C23×C5—22no—
415C23×C5—22no—
416C23×C5—22no—
417C23×C5—22no—
418C23×C5—22no—
419C23×C5—22no—
420C23×C5—22no—
421C23×C5—22no—
422C23×C5—41no—
423C23×C5—41no—
424C23×C5—41no—
425C23×C5—41no—
426C23×C5—41no—
427C23×C5—41no—
428C23×C5—41no—
429C23×C5—41no—
430C23×C5—41no—
431C23×C5—41no—
432C23×C5—41no—
433C23×C5—41no—
434C23×C5—41no—
435C23×C5—41no—
436C23×C5—41no—
437C23×C5—41no—
438C23×C5—41no—
439C23×C5—41no—
440C23×C5—41no—
441C23×C5—41no—
442C23×C5—41no—
443C23×C5—41no—
444C23×C5—41no—
445C23×C5—41no—
446C23×C5—41no—
447C23×C5—41no—
448C23×C5—41no—
449C23×C5—41no—
450C23×C5—41no—
451C23×C5—41no—
452C23×C5—41no—
453C23×C5—41no—
454C23×C5C4×D414yes—
455C23×C5C4×D414yes—
456C23×C5C23×C411yescharacteristic
457C23×C5C22×D411yescharacteristic
458C23×C5C22×D411yescharacteristic
459C23×C5C22×D411yescharacteristic
460C23×C5C22×D411yescharacteristic
461C23×C5C2×#4111yescharacteristic
462C23×C5C2×#4111yescharacteristic
463C23×C5C2×#4111yescharacteristic
464C23×C5C2×#4111yescharacteristic
465C23×C5C2×#4111yescharacteristic
466C23×C5C2×#4111yescharacteristic
467C23×C5H(5,𝔽2)11yescharacteristic
468C23×C5H(5,𝔽2)11yescharacteristic
469C23×C52−1+411yescharacteristic
470C23×C52−1+411yescharacteristic
471C5×D4—232no—
472C2×C4×C5—22no—
473C2×C4×C5—22no—
474C2×C4×C5—22no—
475C2×C4×C5—22no—
476C2×C4×C5—22no—
477C2×C4×C5—22no—
478C2×C4×C5—22no—
479C2×C4×C5—22no—
480C2×C4×C5—22no—
481C2×C4×C5—22no—
482C2×C4×C5—22no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—22no—
486C2×C4×C5—22no—
487C2×C4×C5—22no—
488C2×C4×C5—22no—
489C2×C4×C5—22no—
490C2×C4×C5—22no—
491C2×C4×C5—22no—
492C2×C4×C5—22no—
493C2×C4×C5—22no—
494C2×C4×C5—22no—
495C2×C4×C5—22no—
496C2×C4×C5—22no—
497C2×C4×C5—22no—
498C2×C4×C5—22no—
499C2×C4×C5—22no—
500C2×C4×C5—22no—
501C2×C4×C5—22no—
502C2×C4×C5—22no—
503C2×C4×C5—22no—
504C2×C4×C5—22no—
505C2×C4×C5—22no—
506C2×C4×C5—22no—
507C2×C4×C5—22no—
508C2×C4×C5—22no—
509C2×C4×C5—22no—
510C2×C4×C5—22no—
511C2×C4×C5—22no—
512C2×C4×C5—22no—
513C2×C4×C5—22no—
514C2×C4×C5—22no—
515C2×C4×C5—22no—
516C2×C4×C5—22no—
517C2×C4×C5—416no—
518C2×C4×C5—416no—
519C2×C4×C5—41no—
520C2×C4×C5—41no—
521C2×C4×C5—41no—
522C2×C4×C5—41no—
523C2×C4×C5—41no—
524C2×C4×C5—41no—
525C2×C4×C5—41no—
526C2×C4×C5—41no—
527C2×C4×C5—41no—
528C2×C4×C5—41no—
529C2×C4×C5—41no—
530C2×C4×C5—41no—
531C2×C4×C5—41no—
532C2×C4×C5—41no—
533C2×C4×C5—41no—
534C2×C4×C5—41no—
535C2×C4×C5—41no—
536C2×C4×C5—41no—
537C2×C4×C5—41no—
538C2×C4×C5—41no—
539C2×C4×C5—41no—
540C2×C4×C5—41no—
541C2×C4×C5—41no—
542C2×C4×C5—41no—
543C2×C4×C5—41no—
544C2×C4×C5—41no—
545C2×C4×C5—41no—
546C2×C4×C5—41no—
547C2×C4×C5—41no—
548C2×C4×C5—41no—
549C2×C4×C5—41no—
550C2×C4×C5—41no—
551C2×C4×C5—41no—
552C2×C4×C5—41no—
553C2×C4×C5—41no—
554C2×C4×C5—41no—
555C2×C4×C5—41no—
556C2×C4×C5—41no—
557C2×C4×C5—41no—
558C2×C4×C5—41no—
559C2×C4×C5—41no—
560C2×C4×C5—41no—
561C2×C4×C5C4×D414yes—
562C2×C4×C5C4×D414yescomplemented
563C2×C4×C5#12014yes—
564C2×C4×C5#12114yes—
565C25C23×C511yescharacteristic
566C25C23×C511yescharacteristic
567C22×D4—22no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—22no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4C2×C4×C514yes—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4—41no—
586C23×C4—41no—
587C23×C4C5×D414yes—
588C23×C4C23×C511yescharacteristic
589C23×C4C23×C511yescharacteristic
590C23×C4C23×C511yescharacteristic
591C23×C4C23×C511yescharacteristic
592C23×C4C23×C511yescharacteristic
593C23×C4C23×C511yescharacteristic
594C23×C4C23×C511yescharacteristic
595C23×C4C23×C511yescharacteristic
596C23×C4C23×C511yescharacteristic
597C23×C4C23×C511yescharacteristic
598C23×C4C23×C511yescharacteristic
599C23×C4C23×C511yescharacteristic
600C23×C4C23×C511yescharacteristic
601C4×D4—232no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—41no—
615C2×C4⋊C4C2×C4×C514yescomplemented
616C2×C4⋊C4C5×D414yes—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—41no—
639C2×C22⋊C4—41no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4C2×C4×C514yescomplemented
643C2×C22⋊C4C2×C4×C514yescomplemented
644C2×C22⋊C4C2×C4×C514yescomplemented
645C2×C22⋊C4C2×C4×C514yescomplemented
646C2×C22⋊C4C5×D414yes—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—22no—
650C2×C42—22no—
651C2×C42—22no—
652C2×C42—22no—
653C2×C42—22no—
654C2×C42—41no—
655C2×C42—41no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—22no—
666#95—22no—
667#95—41no—
668#95C2×C4×C514yescomplemented
669#95C5×D414yescomplemented
670C22×C5—24no—
671C22×C5—24no—
672C22×C5—24no—
673C22×C5—24no—
674C22×C5—24no—
675C22×C5—24no—
676C22×C5—42no—
677C22×C5—42no—
678C22×C5—42no—
679C22×C5—42no—
680C22×C5—42no—
681C22×C5—42no—
682C22×C5—42no—
683C22×C5—42no—
684C22×C5—42no—
685C22×C5—42no—
686C22×C5—42no—
687C22×C5—42no—
688C22×C5—42no—
689C22×C5—42no—
690C22×C5—42no—
691C22×C5—42no—
692C22×C5—42no—
693C22×C5—42no—
694C22×C5—42no—
695C22×C5—42no—
696C22×C5—42no—
697C22×C5—42no—
698C22×C5—42no—
699C22×C5—42no—
700C22×C5C2×C4×D411yescharacteristic
701C22×C5C2×C4×D411yescharacteristic
702C22×C5C2×C4×D411yescharacteristic
703C22×C5C2×C4×D411yescharacteristic
704C22×C5C4×#4111yescharacteristic
705C22×C5#52011yescharacteristic
706C22×C5#52011yescharacteristic
707C22×C5C2×#12011yescharacteristic
708C22×C5C2×#12111yescharacteristic
709C22×C5#52511yescharacteristic
710C22×C5#52511yescharacteristic
711C22×C5#52511yescharacteristic
712C22×C5#52511yescharacteristic
713C22×C5#52911yescharacteristic
714C22×C5#53211yescharacteristic
715C22×C5#53411yescharacteristic
716C22×C5#53611yescharacteristic
717C22×C5#53911yescharacteristic
718C22×C5#53911yescharacteristic
719C22×C5D4211yescharacteristic
720C22×C5D4211yescharacteristic
721C22×C5#54611yescharacteristic
722C22×C5#54611yescharacteristic
723C22×C5#54711yescharacteristic
724C22×C5#54711yescharacteristic
725C22×C5#54711yescharacteristic
726C22×C5#54811yescharacteristic
727C22×C5#54811yescharacteristic
728C22×C5#54811yescharacteristic
729C22×C5#55111yescharacteristic
730C22×C5#55211yescharacteristic
731C22×C5#55311yescharacteristic
732C22×C5#55311yescharacteristic
733C22×C5#55611yescharacteristic
734C22×C5#55911yescharacteristic
735C4×C5—24no—
736C4×C5—24no—
737C4×C5—24no—
738C4×C5—24no—
739C4×C5—42no—
740C4×C5—42no—
741C4×C5—42no—
742C4×C5—42no—
743C4×C5—42no—
744C4×C5—42no—
745C4×C5—42no—
746C4×C5—81no—
747C4×C5—81no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24C22×C4×C512yes—
773C24C22×C4×C512yes—
774C24C2×C5×D412yes—
775C24C2×C5×D412yes—
776C24C5×#4112yes—
777C24C5×#4112yes—
778C24C24×C511yescharacteristic
779C2×D4—28no—
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—28no—
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—28no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—28no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—28no—
846C22×C4—28no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4C22×C4×C512yes—
873C22×C4C22×C4×C512yes—
874C22×C4C22×C4×C512yes—
875C22×C4C22×C4×C512yes—
876C22×C4C22×C4×C512yes—
877C22×C4C2×C5×D412yes—
878C22×C4C2×C5×D412yes—
879C22×C4C2×C5×D412yes—
880C22×C4C2×C5×D412yes—
881C22×C4C2×C5×D412yes—
882C22×C4C2×C5×D412yes—
883C22×C4C2×C5×D412yes—
884C22×C4C2×C5×D412yes—
885C22×C4C2×C5×D412yes—
886C22×C4C2×C5×D412yes—
887C22×C4C5×#4112yes—
888C22×C4C5×#4112yes—
889C22×C4C5×#4112yes—
890C22×C4C5×#4112yes—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C42—28no—
907C42—44no—
908C42—44no—
909C2×C5—44no—
910C2×C5—44no—
911C2×C5C4×#12011yescharacteristic
912C2×C5C4×#12111yescharacteristic
913C2×C5#232211yescharacteristic
914C2×C5#235911yescharacteristic
915C2×C5#236111yescharacteristic
916C2×C5#236111yescharacteristic
917C2×C5#236711yescharacteristic
918C2×C5#241011yescharacteristic
919C2×C5#241511yescharacteristic
920C2×C5#243211yescharacteristic
921C2×C5#245511yescharacteristic
922C2×C5#246011yescharacteristic
923C2×C5#246311yescharacteristic
924C2×C5#246611yescharacteristic
925C2×C5#260211yescharacteristic
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23C4×C5×D414yes—
995C23C4×C5×D414yes—
996C23C23×C4×C511yescharacteristic
997C23C22×C5×D411yescharacteristic
998C23C22×C5×D411yescharacteristic
999C23C22×C5×D411yescharacteristic
1000C23C22×C5×D411yescharacteristic
1001C23C2×C5×#4111yescharacteristic
1002C23C2×C5×#4111yescharacteristic
1003C23C2×C5×#4111yescharacteristic
1004C23C2×C5×#4111yescharacteristic
1005C23C2×C5×#4111yescharacteristic
1006C23C2×C5×#4111yescharacteristic
1007C23C5×H(5,𝔽2)11yescharacteristic
1008C23C5×H(5,𝔽2)11yescharacteristic
1009C23C5×2−1+411yescharacteristic
1010C23C5×2−1+411yescharacteristic
1011D4—232no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—416no—
1058C2×C4—416no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4C4×C5×D414yes—
1102C2×C4C4×C5×D414yescomplemented
1103C2×C4C5×#12014yes—
1104C2×C4C5×#12114yes—
1105C5#1418511yescharacteristic, direct product factor, Sylow
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22C2×C4×C5×D411yescharacteristic
1137C22C2×C4×C5×D411yescharacteristic
1138C22C2×C4×C5×D411yescharacteristic
1139C22C2×C4×C5×D411yescharacteristic
1140C22C4×C5×#4111yescharacteristic
1141C22C5×#52011yescharacteristic
1142C22C5×#52011yescharacteristic
1143C22C2×C5×#12011yescharacteristic
1144C22C2×C5×#12111yescharacteristic
1145C22C5×#52511yescharacteristic
1146C22C5×#52511yescharacteristic
1147C22C5×#52511yescharacteristic
1148C22C5×#52511yescharacteristic
1149C22C5×#52911yescharacteristic
1150C22C5×#53211yescharacteristic
1151C22C5×#53411yescharacteristic
1152C22C5×#53611yescharacteristic
1153C22C5×#53911yescharacteristic
1154C22C5×#53911yescharacteristic
1155C22C5×D4211yescharacteristic
1156C22C5×D4211yescharacteristic
1157C22C5×#54611yescharacteristic
1158C22C5×#54611yescharacteristic
1159C22C5×#54711yescharacteristic
1160C22C5×#54711yescharacteristic
1161C22C5×#54711yescharacteristic
1162C22C5×#54811yescharacteristic
1163C22C5×#54811yescharacteristic
1164C22C5×#54811yescharacteristic
1165C22C5×#55111yescharacteristic
1166C22C5×#55211yescharacteristic
1167C22C5×#55311yescharacteristic
1168C22C5×#55311yescharacteristic
1169C22C5×#55611yescharacteristic
1170C22C5×#55911yescharacteristic
1171C4—24no—
1172C4—24no—
1173C4—24no—
1174C4—24no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—42no—
1179C4—42no—
1180C4—42no—
1181C4—42no—
1182C4—81no—
1183C4—81no—
1184C2—44no—
1185C2—44no—
1186C2C4×C5×#12011yescharacteristic
1187C2C4×C5×#12111yescharacteristic
1188C2C5×#232211yescharacteristic
1189C2C5×#235911yescharacteristic
1190C2C5×#236111yescharacteristic
1191C2C5×#236111yescharacteristic
1192C2C5×#236711yescharacteristic
1193C2C5×#241011yescharacteristic
1194C2C5×#241511yescharacteristic
1195C2C5×#243211yescharacteristic
1196C2C5×#245511yescharacteristic
1197C2C5×#246011yescharacteristic
1198C2C5×#246311yescharacteristic
1199C2C5×#246611yescharacteristic
1200C2C5×#260211yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×C5×#389C2semidirect
4. C2×C5×#388C2semidirect
5. C2×C5×#385C2semidirect
6. C2×C5×#385C2semidirect
7. C2×C4×C5×C22⋊C4C2semidirect
8. C5×#1440C2semidirect
9. C5×#1439C2semidirect
11. C5×#1437C2semidirect
12. C5×#1436C2semidirect
13. C5×#1436C2semidirect
14. C5×#1436C2semidirect
15. C5×C22⋊#95C2semidirect
40. C5×#394C4semidirect
60. #14185C5direct (N × H)
111. C2×C5×C4⋊C4C2×C4semidirect
138. C2×C5×C22⋊C4C2×C4semidirect
139. C2×C5×C22⋊C4C2×C4semidirect
140. C2×C5×C22⋊C4C2×C4semidirect
141. C2×C5×C22⋊C4C2×C4semidirect
164. C5×#95C2×C4semidirect
165. C5×#95D4semidirect
168. C2×#389C2×C5semidirect
169. C2×#388C2×C5semidirect
170. C2×#385C2×C5semidirect
171. C2×#385C2×C5semidirect
172. C2×C4×C22⋊C4C2×C5semidirect
173. #1440C2×C5semidirect
174. #1439C2×C5semidirect
176. #1437C2×C5semidirect
177. #1436C2×C5semidirect
178. #1436C2×C5semidirect
179. #1436C2×C5semidirect
180. C22⋊#95C2×C5semidirect
366. #394C4×C5semidirect
562. C2×C4×C5C4×D4semidirect
615. C2×C4⋊C4C2×C4×C5semidirect
642. C2×C22⋊C4C2×C4×C5semidirect
643. C2×C22⋊C4C2×C4×C5semidirect
644. C2×C22⋊C4C2×C4×C5semidirect
645. C2×C22⋊C4C2×C4×C5semidirect
668. #95C2×C4×C5semidirect
669. #95C5×D4semidirect
1102. C2×C4C4×C5×D4semidirect
1105. C5#14185direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C4×C5×D42
C2×C5×#3942
C2×C5×#3892
C2×C5×#3882
C2×C5×#3852
C2×C4×C5×C22⋊C42
C5×#14402
C5×#14392
C5×#14382
C5×#14372
C5×#14362
C5×C22⋊#952
#141855